Solving for base angles in a congruent triangle

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Homework Help Overview

The discussion revolves around solving for the base angles in a congruent triangle, where one base angle is expressed as 3x + 5, the other base angle is unknown, and the remaining angle is given as x + 16. Participants are exploring the relationships between these angles and the implications of their equations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the equality of the base angles and the implications of setting 3x + 5 equal to itself. Questions arise about the number of unknowns and equations available for solving the problem.

Discussion Status

There is an ongoing exploration of the relationships between the angles, with some participants suggesting the need for additional information to formulate a solvable equation. The concept of the sum of angles in a triangle being 180 degrees is mentioned as a potential avenue for further investigation.

Contextual Notes

Participants question the terminology used, specifically the reference to a "congruent triangle" versus "isosceles triangle," indicating a need for clarity in definitions. There is also an acknowledgment of the constraints posed by having multiple unknowns with limited equations.

tomtomtom1
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Homework Statement



Solving for base angles in a congruent triangle
One of the base angles in a congruent triangle is 3x+5
The other base angle is unknown
The remaining angle is x+16.

Homework Equations



See attached PDF

The Attempt at a Solution



Because two base angles in a congruent triangle are the same and I have been given one of them I did the following:-

3x+5 = 3x+5 (I then tried to solve for x but this cancels out to 0.)

I want to know why this is the case, i think it is because i have 2 unknown variables but only1 equation.
 

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tomtomtom1 said:

Homework Statement



Solving for base angles in a congruent triangle
One of the base angles in a congruent triangle is 3x+5
The other base angle is unknown
The remaining angle is x+16.

Homework Equations



See attached PDF

The Attempt at a Solution



Because two base angles in a congruent triangle are the same and I have been given one of them I did the following:-

3x+5 = 3x+5 (I then tried to solve for x but this cancels out to 0.)

I want to know why this is the case, i think it is because i have 2 unknown variables but only1 equation.

As you said, the other base angle is 3x+5. You need to use something else. What's the sum of all of the angles of a triangle?
 
The sum of the interior angles of a triangle is 180Degrees.

But i want to know if making 3x+5 equal to itself 3x+5 (3x+5 = 3x+5) am i trying to solve for 1 unknown with 1 equation or am i trying to solve 2 unknowns with 1 equations?
 
Setting 3x + 5 equal to itself implies 1 = 1. You need some other piece of information.
 
tomtomtom1 said:
The sum of the interior angles of a triangle is 180Degrees.

But i want to know if making 3x+5 equal to itself 3x+5 (3x+5 = 3x+5) am i trying to solve for 1 unknown with 1 equation or am i trying to solve 2 unknowns with 1 equations?

As you said, the sum of your angles is 180 degrees. Write down an equation that expresses that.
 
Also, why are you calling it a "congruent triangle"? Don't you mean "isoceles triangle"?

To expand on what others have said, what is the sum of the 3 angles in terms of x? Equate that expression to 180 degrees and solve.
 

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